Explainable molecular property prediction is essential for various scientific fields, such as drug discovery and material science. Despite delivering intrinsic explainability, linear models struggle with capturing complex, non-linear patterns. Large language models (LLMs), on the other hand, yield accurate predictions through powerful inference capabilities yet fail to provide chemically meaningful explanations for their predictions. This work proposes a novel framework, called MoleX, which leverages LLM knowledge to build a simple yet powerful linear model for accurate molecular property prediction with faithful explanations. The core of MoleX is to model complicated molecular structure-property relationships using a simple linear model, augmented by LLM knowledge and a crafted calibration strategy. Specifically, to extract the maximum amount of task-relevant knowledge from LLM embeddings, we employ information bottleneck-inspired fine-tuning and sparsity-inducing dimensionality reduction. These informative embeddings are then used to fit a linear model for explainable inference. Moreover, we introduce residual calibration to address prediction errors stemming from linear models' insufficient expressiveness of complex LLM embeddings, thus recovering the LLM's predictive power and boosting overall accuracy. Theoretically, we provide a mathematical foundation to justify MoleX's explainability. Extensive experiments demonstrate that MoleX outperforms existing methods in molecular property prediction, establishing a new milestone in predictive performance, explainability, and efficiency. In particular, MoleX enables CPU inference and accelerates large-scale dataset processing, achieving comparable performance 300x faster with 100,000 fewer parameters than LLMs. Additionally, the calibration improves model performance by up to 12.7% without compromising explainability.